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I need help.

What is the difference between

[tex]

\int_{0}^b x^2 dx

[/tex]

with

[tex]

lim_{b\rightarrow \ \infty} \int_{0}^b x^2 dx

[/tex]

???

Can someone please show me algebraically for its clarity?

I don’t understand of the 2nd integral equation means.

Especially the appears of limit as b approach to infinity.

Thanks in advance